Theorem nfcoll

Description: Bound-variable hypothesis builder for the collection operation. (Contributed by Rohan Ridenour, 11-Aug-2023)

	Ref	Expression
Hypotheses	nfcoll.1	|- F/_ x F
	nfcoll.2	|- F/_ x A
Assertion	nfcoll	|- F/_ x ( F Coll A )

Proof

Step	Hyp	Ref	Expression
1		nfcoll.1	|- F/_ x F
2		nfcoll.2	|- F/_ x A
3		df-coll	|- ( F Coll A ) = U_ y e. A Scott ( F " { y } )
4		nfcv	|- F/_ x { y }
5	1 4	nfima	|- F/_ x ( F " { y } )
6	5	nfscott	|- F/_ x Scott ( F " { y } )
7	2 6	nfiun	|- F/_ x U_ y e. A Scott ( F " { y } )
8	3 7	nfcxfr	|- F/_ x ( F Coll A )